Computer Finds New Math 'Jewel' In The Rough
The formula for finding Mersenne primes.
A computer professional in Norway, with the help of an online computing project, has discovered a new Mersenne prime. This sought-after number represents the 47th Mersenne prime discovered since ancient Greek mathematicians first uncovered them.
These primes are called the "jewels" of number theory, and it takes a huge computing system about two or three weeks to test a single number to see if it could lead to a Mersenne prime.
For those of you for whom basic math is a distant memory, a reminder:
Primes are numbers that are divisible by only the number 1 and themselves. So 2 is prime; so are 3, 5, 7 and so on. The year 2003 was a prime year, and 2011 will be as well.
Not Just Any Prime
Mersenne primes are a special class of prime, and they have a particular formula.
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STEVE INSKEEP, host:
And we have some prime news this morning. Drum roll, please.
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INSKEEP: Thank you very much. A computer professional in Norway has discovered a new Mersenne prime - what you and I might call a prime number. This discovery brings joy to prime number fans worldwide and brings a special satisfaction to NPR's Joe Palca. He'll tell you why.
JOE PALCA: For those of you for whom basic math is a distant memory, we begin with a reminder. Primes are numbers that are divisible by only one and themselves. So, two is prime. So is three, five, seven and so on. 2003 was a prime year. So will be 2011.
Mersenne primes have been called the jewels of number theory. They are a special class of prime, and they have a particular formula. I will now tell you the formula. And let me warn you: Only trained professionals should attempt to give mathematical formulas over the radio. Here goes.
It is two raised to the nth power minus one, where n is itself a prime number and the result is prime. Ancient Greek mathematicians were the first to describe Mersenne primes. So far, only 46 have been discovered - or now, I should say 47, because there's a new one, and it's a whopper: nearly 13 million digits long.
It was found as part of the Great Internet Mersenne Prime Search, or GIMPS. GIMPS involves tens of thousands of computers churning away, looking for new Mersenne primes. Mathematician Chris Caldwell of the University of Tennessee Martin says finding Mersenne primes takes a lot of computing power.
Professor CHRIS CALDWELL (Math, University of Tennessee Martin): Not only do you have to multiply a 13-million-digit number times a 13-million-digit number, you have to do that about 13 million times. That just takes a tremendous amount of computation.
PALCA: When I first reported on the Great Internet Mersenne Prime Search last April 10th, I exhorted NPR listeners to download the software and join the effort. The new Mersenne prime was discovered by someone who was already a prime hunter. Odd Magnar Strindmo from Melhus, Norway, has been part of GIMPS since it began in 1996.
Now, finding a new Mersenne prime is exciting all by itself, but it's especially exciting because of a bet I made with George Woltman. He's the man who runs the Great Internet Mersenne Prime Search. I bet the next one would be found before 2012, helped along by all those NPR listeners who I hoped would download the program.
Woltman emailed me, saying he felt a little silly losing the bet so soon. But I have a confession to make: I meant the next largest Mersenne prime. The 47th Mersenne prime is actually 141,125 digits smaller than one that was discovered last year.
So, I won on a technicality, and I'm willing to carry on the bet until the largest one is found. After all, we didn't bet any money, so I can afford to be magnanimous.
Joe Palca, NPR News.
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INSKEEP: And you could learn more about the new prime by going to our Web site - our prime Web site: npr.org.
This is NPR News. Transcript provided by NPR, Copyright National Public Radio.
